Point-wise estimation for anisotropic densities

被引：18

作者：

Liu, Youming ^{[1
]}

Wu, Cong ^{[1
]}

机构：

[1] Beijing Univ Technol, Dept Appl Math, Beijing 100124, Peoples R China

来源：

JOURNAL OF MULTIVARIATE ANALYSIS | 2019年 / 171卷

基金：

中国国家自然科学基金; 北京市自然科学基金;

关键词：

Adaptivity; Anisotropic density; Local Holder condition; Optimality; Point-wise estimation; WARPED BASES; CONVERGENCE;

D O I：

10.1016/j.jmva.2018.11.014

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

This paper considers point-wise estimation of density functions under the local anisotropic Holder condition by the wavelet method. A linear wavelet estimate is first introduced and shown to be optimal. A data driven version is provided for adaptivity and the influence of the dimension is reduced under the independence structure of the estimated density. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：112 / 125

页数：14

共 21 条

[1] The adaptive rate of convergence in a problem of pointwise density estimation [J].

Butucea, C .

STATISTICS & PROBABILITY LETTERS, 2000, 47 (01) :85-90

[2]

butucea c., 2001, ESAIM Probab. Statist., V5, P1

[3] Warped bases for conditional density estimation [J].

Chagny G. .

Mathematical Methods of Statistics, 2013, 22 (4) :253-282

[4] PENALIZATION VERSUS GOLDENSHLUGER-LEPSKI STRATEGIES IN WARPED BASES REGRESSION [J].

Chagny, Gaelle .

ESAIM-PROBABILITY AND STATISTICS, 2013, 17 :328-358

[5] Anisotropic adaptive kernel deconvolution [J].

Comte, F. ;

Lacour, C. .

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2013, 49 (02) :569-609

[6] On minimax wavelet estimators [J].

Delyon, B ;

Juditsky, A .

APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 1996, 3 (03) :215-228

[7] Approximation methods for supervised learning [J].

DeVore, R ;

Kerkyacharian, G ;

Picard, D ;

Temlyakov, V .

FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 2006, 6 (01) :3-58

[8]

Donoho DL, 1996, ANN STAT, V24, P508

[9]

DOUKHAN P, 1990, CR ACAD SCI I-MATH, V310, P425

[10] On adaptive minimax density estimation on Rd [J].

Goldenshluger, A. ;

Lepski, O. .

PROBABILITY THEORY AND RELATED FIELDS, 2014, 159 (3-4) :479-543

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